Electrical filters have long been used in the processing of electrical signals. In particular, such electrical filters are used to select desired electrical signal frequencies from an input signal by passing the desired signal frequencies, while blocking or attenuating other undesirable electrical signal frequencies. Filters may be classified in some general categories that include low-pass filters, high-pass filters, band-pass filters, and band-stop filters, indicative of the type of frequencies that are selectively passed by the filter. Further, filters can be classified by type, such as Butterworth, Chebyshev, Inverse Chebyshev, and Elliptic, indicative of the type of bandshape frequency response (frequency cutoff characteristics).
The type of filter used often depends upon the intended use. In communications applications, band pass and band stop filters are conventionally used in cellular base stations, cell phone handsets, and other telecommunications equipment to filter out or block RF signals in all but one or more predefined bands. Of most particular importance is the frequency range from approximately 500-3,500 MHz.
With reference to FIG. 1 a prior art telecommunications system 10 may include a transceiver 12 capable of transmitting and receiving wireless signals, and a controller/processor 14 capable of controlling the functions of the transceiver 12.
The transceiver 12 generally comprises a broadband antenna 16, a duplexer 18 having a transmit filter 24 and a receive filter 26, a transmitter 20 coupled to the antenna 16 via the transmit filter 24 of the duplexer 18, and a receiver 22 coupled to the antenna 16 via the receive filter 26 of the duplexer 18.
The transmitter 20 includes an upconverter 28 configured for converting a baseband signal provided by the controller/processor 14 to a radio frequency (RF) signal, a variable gain amplifier (VGA) 30 configured for amplifying the RF signal, a bandpass filter 32 configured for outputting the RF signal at an operating frequency selected by the controller/processor 14, and a power amplifier 34 configured for amplifying the filtered RF signal, which is then provided to the antenna 16 via the transmit filter 24 of the duplexer 18.
The receiver 22 includes a notch or stopband filter 36 configured for rejecting transmit signal interference from the RF signal input from the antenna 16 via the receiver filter 26, a low noise amplifier (LNA) 38 configured for amplifying the RF signal from the stop band filter 36 with a relatively low noise, a tunable bandpass filter 40 configured for outputting the amplified RF signal at a frequency selected by the controller/processor 14, and a downconverter 42 configured for downconverting the RF signal to a baseband signal that is provided to the controller/processor 14. Alternatively, the function of rejecting transmit signal interference performed by the stop-band filter 36 can instead be performed by the duplexer 18. Or, the power amplifier 34 of the transmitter 20 can be designed to reduce the transmit signal interference.
It should be appreciated that the block diagram illustrated in FIG. 1 is functional in a nature, and that several functions can be performed by one electronic component or one function can be performed by several electronic components. For example, the functions performed by the up converter 28, VGA 30, bandpass filter 40, downconverter 42, and controller/processor 14 are oftentimes performed by a single transceiver chip. The function of the bandpass filter 32 can be into the power amplifier 34 and the transmit filter 24 of the duplexer 18.
Microwave filters are generally built using two circuit building blocks: a plurality of resonators, which store energy very efficiently at a resonant frequency (which may be a fundamental resonant frequency f0 or any one of a variety of higher order resonant frequencies f1-fn); and couplings, which couple electromagnetic energy between the resonators to form multiple reflection zeros providing a broader spectral response. For example, a four-resonator filter may include four reflection zeros. For the purposes of this specification, a reflection zero may refer to the roots of a filter's reflection function where the inductance and capacitance cancel and a minimum amount of power is reflected. The strength of a given coupling is determined by its reactance (i.e., inductance and/or capacitance). The relative strengths of the couplings determine the filter shape, and the topology of the couplings determines whether the filter performs a band-pass or a band-stop function. The resonant frequency f0 is largely determined by the inductance and capacitance of the respective resonator. For conventional filter designs, the frequency at which the filter is active is determined by the resonant frequencies of the resonators that make up the filter. Each resonator must have very low internal resistance to enable the response of the filter to be sharp and highly selective for the reasons discussed above. This requirement for low resistance tends to drive the size and cost of the resonators for a given technology.
The front-end receive filter (e.g., the receive filter 26 illustrated in FIG. 1) preferably takes the form of a sharply defined band-pass filter to eliminate various adverse effects resulting from strong interfering signals at frequencies near the desired received signal frequency. Because of the location of the front-end receiver filter at the antenna input, the insertion loss must be very low so as to not degrade the noise figure. In most filter technologies, achieving a low insertion loss requires a corresponding compromise in filter steepness or selectivity. In practice, most filters for cell phone handsets are constructed using acoustic resonator technology, such as surface acoustic wave (SAW), bulk acoustic wave (BAW), and film bulk acoustic resonator (FBAR) technologies. Such acoustic resonator filters have the advantages of low insertion loss, compact size, and low cost compared to equivalent inductor/capacitor resonators.
Design of practical microwave filters may begin with the design of an initial circuit generated, for instance, using image design or network synthesis design. These approaches generally, from the outset, only consider circuits with the fewest possible number of circuit elements. This is generally performed from a desire to minimize losses in the final filter, and may be a common practice in microwave filter design of all types. The initial design may be generated using simplified, idealized circuit element models, which may typically ignore losses and other unwanted characteristics of the physical circuit elements used to make the final filter. Computer optimization may be a critical and necessary step in the design of practical microwave filters. Design tools including Agilent Advanced Design System (ADS), among others, may use numerical optimization methods, such as Monte Carlo, gradient, etc., to improve the “initial circuit design.” This computer optimization step may use increasingly realistic, accurate circuit element models and may restrict circuit element values to those that can be manufactured in accordance with the final filter design. The optimization may search for the combination of circuit element values that best matches the desired filter response. This type of computer optimization may be often used in microwave filter design. Although the optimization may generally produce a significantly improved design that may be realized with physical circuit elements, it generally does not reduce the number of circuit elements in the final circuit design from the number of circuit elements in the initial circuit design, nor does it change one type of circuit element into another.
For example, one initial circuit that is typically used in the design of acoustic wave band-pass filters is a ladder filter 50, which comprises a number of alternating shunt resonators 52a and series resonators 52b, as illustrated in FIG. 2. The filter 50 can be considered an N resonator ladder topology (i.e., N equals the number of resonators, and in this case 6). For the purposes of this specification, an acoustic ladder filter may refer to one or more filters using the Mason-type acoustic wave ladder circuit structure comprising alternating series and shunt acoustic wave resonators.
Each of the acoustic resonators 52 may be described by a modified Butterworth-Van Dyke (MBVD) model 54. MBVD models 54 may also describe SAW resonators, which may be fabricated by disposing interdigital transducers (IDTs) on a piezoelectric substrate, such as crystalline Quartz, Lithium Niobate (LiNbO3), Lithium Tantalate (LiTaO3) crystals or BAW resonators. Each MBVD model 54 includes a motional capacitance Cm 56, a static capacitance C0 58, a motional inductance Lm 60, and a resistance R 62. The motional capacitance Cm 56 and motional inductance Lm 60 may result from the interactions of electrical and acoustical behavior, and thus, may be referred to as the motional arm of the MBVD model 54. The static capacitance C0 58 may result from the inherent capacitance of the structure, and thus, may be referred to as the static (non-motional) capacitance of the MBVD model 54. The resistance R 62 may result from the electrical resistance of the acoustic resonator 52. The parameters are related by the following equations:
                                          ω            E                    =                      1                                                            L                  m                                ⁢                                  C                  m                                                                    ;                            [        1        ]                                                                    ω              A                                      ω              R                                =                                    1              +                              1                γ                                                    ,                            [        2        ]            where ωR and ωA may be the respective resonance and anti-resonance frequencies for any given acoustic resonator, and gamma γ may depend on a material's property, which may be further defined by:
                                          C            0                                C            m                          =                  γ          .                                    [        3        ]            Typical γ values may range from about 12 to about 18 for 42-degree X Y cut LiTaO3.
It can be appreciated from equation [1] that the resonant frequency of each of the acoustic resonators 52 will depend on the motional arm of the MBVD model 54, whereas the filter characteristics (e.g., bandwidth) will be determined by γ in equation [2]. The Quality factor (Q) for an acoustic resonator 52 may be an important figure of merit in acoustic filter design, relating to the loss of the element within the filter. Q of a circuit element represents the ratio of the energy stored per cycle to the energy dissipated per cycle. The Q factor models the real loss in each acoustic resonator 52, and generally more than one Q factor may be required to describe the loss in an acoustic resonator 52. Q factors may be defined as follows for the filter examples. The motional capacitance Cm 56 may have an associated Q defined as QCm=1.0E+8; the static capacitance C0 58 may have an associated Q defined as QC0=200; and motional inductance Lm 60 may have an associated Q defined as QLm=1000. Circuit designers may typically characterize SAW resonators by resonant frequency ωR, static capacitance C0, gamma γ, and Quality factor QLm. For commercial applications, QLm may be about 1000 for SAW resonators, and about 3000 for BAW resonators.
The frequency response for the filter 50 is illustrated in FIG. 3 which presents the scattering matrices |S21|2 (insertion loss) and |S11|2 (return loss) for the filter response in logarithmic units of decibels (dB) versus frequency f. Let the resonance and anti-resonance frequencies of each of the shunt resonators 52a be respectively designated as ωrp and ωap, and the resonance and anti-resonance frequencies of each of the series resonators 52b be respectively designated as ωrs and ωas. When ωrs and ωap are approximately equal to each other, a passband centered near ω=ωrp, ωap is created, and transmission zeroes at ω=ωrp, ωas defining the passband edges are created, as shown in the filter response illustrated in FIG. 3. For the purposes of this specification, a transmission zero may refer to the roots of a filter's transmission function where a maximum amount of power is reflected. At frequencies f far from the passband center frequency ωp the resonators act approximately as capacitors, resulting in a |S21|2 filter response that forms wings that becomes asymptotically constant for large |ω−ωp|, providing the out-of-band rejection.
A band pass filter response may be characterized by the return loss (i.e., the value of the |S11|2 at the center passband frequency ωp), insertion loss (i.e., the value of |S21|2 at the center passband frequency ωp, the passband width (PBW), and the out-of-band rejections ε (i.e., 1/|S21| at a large |ω−ωp|). Band pass ladder filters can be designed only over a limited accessible range of these parameters, with the range depending on the material parameter value γ and the number of resonators (termed the filter order). The material parameter values γ for currently widely used materials for SAW and BAW filters are in the range of 12-14, allowing the resonance frequency and antiresonance frequency to be close to the passband center frequency ωp, thereby creating a relatively narrow passband in the |S21|2 filter response. Materials with a material parameter value γ of 4 are currently under development. A smaller material parameter value γ would enable a wider passband width PBW, decrease return loss RL, or improve the out-of-band rejection ε.
For a fixed passband width PBW, as the out-of-band rejection ε increases, the return loss RL decreases. In some cases, passive circuit elements are coupled to the ladder structure to improve filter performance. For example, adding inductors can decrease the effective material parameter value γ, which can increase the passband width PBW, decrease the return loss RL, or improve the out-of-band rejection ε. However, the benefits from the addition of inductors come at the cost of increased insertion loss, size, and cost. The band pass filter parameters are pushed to the limits of the accessible range in order to maximize performance, with tradeoffs between the parameters depending on the system applications and requirements. Higher order filters can achieve greater out-of-band rejection ε at a given passband return loss RL and passband width PBW.
As briefly discussed above, the filter 50 may have an initial circuit design, which may then be optimized via a suitable computer optimization technique (e.g., Agilent ADS software) to create a final circuit design. For example, the filter 50 may initially be designed with the resonant frequencies ωR and static capacitances C0 for each resonator 52 illustrated in FIG. 4a, which when simulated, results in the frequency response illustrated in FIG. 4b. This frequency response is shown characterized by the following markers: M1 of Mag S21=−65.71 dB at frequency=1.770 GHz; M2 of Mag S21=−36.735 dB at frequency=1.830 GHz; M3 of Mag S21=−4.367 dB at frequency=1.850 GHz; M4 of Mag S21=−1.444 dB at frequency=1.879 GHz; M5 of Mag S21=−2.680 dB at frequency=1.910 GHz; M6 of Mag S21=−30.118 dB at frequency=1.930 GHz; and M7 of Mag S21=−62.874 dB at frequency=1.990 GHz.
After optimization, the filter 50 may have the resonant frequencies ωR and static capacitances C0 for each resonator 52 illustrated in FIG. 5a, which when simulated, results in the frequency response illustrated in FIG. 5b. This frequency response is shown characterized by the following markers: N1 of Mag S21=−46.943 dB at frequency=1.770 GHz; N2 of Mag S21=−29.865 dB at frequency=1.829 GHz; N3 of Mag S21=−1.479 dB at frequency=1.851 GHz; N4 of Mag S21=−0.833 dB at frequency=1.875 GHz; N5 of Mag S21=−1.898 dB at frequency=1.910 GHz; N6 of Mag S21=−41.977 dB at frequency=1.929 GHz; and N7 of Mag S21=−47.182 dB at frequency=1.990 GHz.
As can be appreciated from the foregoing, the values of the MBVD models 54 for the resonators 52 have changed with optimization with improvement in the frequency response. However, the type and number of circuit elements remains unchanged, and thus, does not reduce the footprint or cost of the final circuit. Therefore, for microwave filters generally, and especially filter designs that contain passive elements and/or use more complex design techniques, such as modern network theory or image theory with more complex sections, an improved optimization method is needed.